

A326029


Number of strict integer partitions of n whose mean and geometric mean are both integers.


8



0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 3, 1, 2, 1, 3, 1, 1, 2, 3, 1, 3, 1, 1, 3, 6, 1, 3, 1, 2, 1, 1, 1, 3, 1, 6, 1, 5, 1, 2, 2, 2, 4, 3, 1, 9, 1, 1, 3, 1, 1, 4, 1, 4, 2, 6, 1, 6, 1, 3, 7, 4, 2, 5, 1, 10, 1, 3, 1, 9, 3
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OFFSET

0,11


LINKS



EXAMPLE

The a(55) = 2 through a(60) = 9 partitions:
(55) (56) (57) (58) (59) (60)
(27,16,9,2,1) (24,18,8,6) (49,7,1) (49,9) (54,6)
(27,25,5) (50,8) (48,12)
(27,18,12) (27,24,9)
(27,24,6,2,1)
(36,12,9,2,1)
(36,9,6,4,3,2)
(24,18,9,6,2,1)
(27,16,9,4,3,1)


MATHEMATICA

Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&IntegerQ[Mean[#]]&&IntegerQ[GeometricMean[#]]&]], {n, 0, 30}]


CROSSREFS

Partitions with integer mean and geometric mean are A326641.
Strict partitions with integer mean are A102627.
Strict partitions with integer geometric mean are A326625.
Nonconstant partitions with integer mean and geometric mean are A326641.
Subsets with integer mean and geometric mean are A326643.
Heinz numbers of partitions with integer mean and geometric mean are A326645.
Cf. A051293, A067538, A067539, A078175, A082553, A316413, A326027, A326623, A326644, A326646, A326647.


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



